Three identical parallel plate (air) capacitors $C_1, C_2, C_3$ have capacitances $C$ each. The space between their plates is now filled with dielectrics as shown. If all the three capacitors, still have equal capacitances, obtain the relation between the dielectric constants $k_1, k_2, k_3$ and $k_4$.

Between the plates of a parallel-plate capacitor of area $A$, a copper plate sits on a dielectric slab of $k=2$, as shown in figure below. Find the equivalent capacitance of this arrangement.

What is the capacitance of arrangement of $4$ plates of area $A$ at distance d in air in Figure below?

What is the capacitance of arrangement of $4$ plates of area $A$ at distance $d$ in air in Figure below?

A capacitor is made of a fiat plate of area $A$ and a second plate having a stair-like structure, as shown in Figure below. The width of each stair is a and the height is $b$Find the capacitance of the assembly.

The plate $A$ of a parallel plate capacitor is connected to a spring of force constant $k$ and can move, while the plate $B$ is fixed. The arrangement is held between two
rigid supports as shown in Figure below. If a charge $+q$ is placed on plate $A$ and $-q$ on plate $B$, by how much does the spring elongate?

Four point charges $Q, q, Q$ and $q$ are placed at the corners of a square of side $\text{'}a\text{'}$ as shown in the figure.

Find the resultant electric force on a charge $Q$.

Four point charges $Q, q, Q$ and $q$ are placed at the corners of a square of side $\text{'}a\text{'}$ as shown in the figure.

Find the potential energy of this system.